Abstract: We present a constructive criterion for flatness of a morphism of analytic spaces (over or ) or, more generally, for flatness over of a coherent sheaf of -modules . The criterion is a combination of a simple linear-algebra condition ``in codimension zero'' and a condition ``in codimension one'' which can be used together with the Weierstrass preparation theorem to inductively reduce the fibre-dimension of the morphism .